# Video: AQA GCSE Mathematics Higher Tier Pack 2 • Paper 1 • Question 29

The diagram shows a sketch of 𝑦 = cos 𝑥° for −180 ≤ 𝑥 ≤ 540. Part a) Write down the coordinates of 𝐴. b) Write down the coordinates of 𝐵.

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### Video Transcript

The diagram shows a sketch of 𝑦 is equal to cos of 𝑥 degrees for negative 180 is less than or equal to 𝑥 which is less than or equal to 540. Part a) Write down the coordinates of 𝐴.

Remember the graph of 𝑦 is equal to cos of 𝑥 is periodic. That means it repeats and it has a period. It repeats every 360 degrees. This is a useful place to start.

We know that the cos graph intersects the 𝑦-axis at one. It gets back to one at 360 degrees. So 360 degrees must be the point on the 𝑥-axis at which the graph reaches one again.

We can halve this. And we now know that the graph reaches negative one at 180. Halving again, it intersects the 𝑥-axis at 90 and then 270. We add 90 to 360. And we can see that it intersects the 𝑥-axis once again at 450 degrees. And the graph is also symmetrical in the 𝑦-axis. So we can add negative 90 and negative 180.

Once we have all of that information written down, we can simply read the coordinates for 𝐴 straight from the graph. 𝐴 has coordinates 180, negative one.

b) Write down the coordinates of 𝐵.

We can see that 𝐵 is the point where the graph intersects the 𝑥-axis for the third time. The coordinates of 𝐵 are 450, zero.

The values on the 𝑥-axis represent an angle there in degrees. So we can say that the coordinates of 𝐴 are 180 degrees, negative one and the coordinates of 𝐵 are 450 degrees, zero.